1. Field of the Invention
This invention relates to a digital signal processing circuit making use of the so-called residue number system ("RNS") system in which the input data expressed by the binary code is processed after conversion thereof into the RNS code which represents the input data by the combination of residues obtained by dividing the input data by plural moduli.
2. Description of the Prior Art
As a digital signal processing circuit, a system of an arithmetic operation making use of the RNS system has been proposed in H. L. Garner, "The Residue Number System", IRE Transactions on Electronic Computers, vol. EL-8, No. 6, June 1959, pages 140 to 147 or in F. J. Taylor, "Residue Arithmetic: A Tutorial With Examples", IEEE Computer, vol. 17, No. 5, May 1984, pages 50 to 61.
With the digital signal processing system making use of the RNS system, the input data represented by the binary code is converted into the RNS code in which the input data is represented by combination of residues obtained upon dividing the input data by plural moduli, and the modulo operation is performed in each of the systems allocated to the respective moduli, so that the carry operation (such as in a binary operation operation) becomes unnecessary to perform at the time of the arithmetic operation. Hence, digital signals can be processed more accurately and at a higher processing speed.
As a digital signal processing system making use of the above mentioned RNB system, there is a digital filter system, as disclosed in "Treatises of Electric Communication Association," '84/4 vol. J67-1, No. 4, pages 536 to 543.
The digital filter apparatus making use of the above mentioned RNS system is constructed as shown in FIG. 1.
The digital filter apparatus of the RNS system shown in FIG. 1 is constituted by an encoder section 40 to which a digital video signal D.sub.BI represented by the binary code is entered, a filter section 60 to which an output of the encoder section 40 is entered, and a decoder section 60 to which an output of the filter section 50 is supplied.
The encoder section 40 is constituted by (n+1) encoders 41, 42, . . . , each of which is formed by a read only memory (ROM) conversion table. The conversion table employed in the above encoders 41, 42, . . . , is constituted by a ROM into which are written residue data R.sub.0, R.sub.1, R.sub.2, . . . , R.sub.n which are obtained by dividing the binary code data by (n+1) positive integers that are prime numbers with respect to one another and which are associated with the moduli m.sub.0, m.sub.1, m.sub.2, . . . , m.sub.n, respectively.
The digital video signal D.sub.BI represented in the binary code, entered into the encoder section 40, is inverted by the encoders 41, 42, . . . making use of the conversion table, into the residue data R.sub.0, R.sub.1, R.sub.2, . . . , R.sub.n, associated with the moduli m.sub.0, m.sub.1, m.sub.2, . . . , m.sub.n, respectively.
When the digital video signal D.sub.BI is entered into the encoder section 40, the RNS code data D.sub.RI represented by the combination of the residue data R.sub.0, R.sub.1, R.sub.2, . . . , R.sub.n produced by the encoders 41, 42, . . . is output from the encoder section 40.
The RNS code data D.sub.RI, output by the encoder section 40, is supplied to the filter section 50.
The filter section 50 is constituted by (n+1) digital filter circuits 51, 52, . . . associated with the coefficients m.sub.0, m.sub.1, m.sub.2, . . . , m.sub.n respectively. Each of the digital filter circuits 51, 52, . . . processes the RNS code data D.sub.RI supplied from the encoder section 40 by a modulo operation for affording the desired same filter characteristics to each of the above residue data R.sub.0, R.sub.1, R.sub.2, . . . , R.sub.n, that is, to each of the moduli m.sub.0, m.sub.1, m.sub.2, . . . , m.sub.n. Meanwhile, the digital filter circuit 51 performs an arithmetic modulo operation on the residue data R.sub.0, the digital filter circuit 52 performs an arithmetic modulo operation on the residue data R.sub.1, and so forth, so that each of the digital filter circuits performs a modulo operation for each of the residue data allocated thereto.
That is, in the filter section 50, each of the digital filter circuits 51, 52, . . . processes the RNS code data D.sub.RI represented by the combination of the residue data R.sub.0, R.sub.1, R.sub.2, . . . , R.sub.n by a separate modulo operation for each of the moduli m.sub.0, m.sub.1, m.sub.2, . . . , m.sub.n, so that the residue data having desired filter characteristics are formed by the digital filter circuits 51, 52, . . . The filter section 50 outputs RNS code data D.sub.RO represented by the combination of the residue data obtained by the digital filter circuits 61, 62, . . . .
The RNS code data D.sub.RO, output by the filter section 50, is supplied to the decoder section 60.
The decoder section 60 is constituted by a conversion table formed by a ROM. The conversion table employed in the decoder section 60 is constituted by a ROM in which the binary code data corresponding to the PNB code data are written as the conversion table data.
This decoder section 60 outputs the RNS code data D.sub.RO supplied from the filter section 60 after conversion into corresponding binary code data D.sub.BO by the above conversion table.
It is noted that the above RNS code data may be converted into the binary code data based on, for example, Son's residue theorem.
According to Son's residue theorem, if the residue r.sub.i of x by a modulus m.sub.i is expressed by a formula (1) EQU r.sub.i =x mod m.sub.i ( 1)
by using a symbol mod, the RNS code data D.sub.RO is expressed by the combination of residue data R.sub.0, R.sub.1, R.sub.2, . . . , R.sub.n by positive integers m.sub.0, m.sub.1, m.sub.2, . . . , m.sub.n, that are prime numbers with respect to a positive integer, and the RNS code data may be demodulated into binary code data having the value B by solving the formula (5) ##EQU1## from the values M, M.sub.i and N.sub.i represented by the formulas (2), (3) and (4) ##EQU2##
The decoder section 60 may be constituted by using a ROM conversion table in which the thus produced binary code data are written as the conversion table data.
In the above described digital filter apparatus shown in FIG. 1, with n=4, m.sub.0 =7, m.sub.1 =11, m.sub.2 =13, m.sub.3 =15 and m.sub.4 =16, as an example, the relation of correspondence between the binary code data D.sub.B and the RNS code data D.sub.R may be represented as shown in the following Table 1.
TABLE 1 ______________________________________ Relation of Correspondence Between Binary Code Data D.sub.B and RNS Code Data D.sub.R with m.sub.0 =7, m.sub.1 =11, m.sub.2 =13, m.sub.3 =15 and m.sub.4 =16 Binary Code RNS Code Data D.sub.R Data D.sub.B m.sub.0 m.sub.1 m.sub.2 m.sub.3 m.sub.4 ______________________________________ 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 7 0 7 7 7 7 1 0 0 0 0 0 5 10 4 10 0 1 0 0 0 0 1 6 0 5 11 1 1 0 0 0 0 2 0 1 6 12 2 1 0 0 0 0 3 1 2 7 13 3 ______________________________________
With the digital filter apparatus, making use of the RNS system, when the binary code data D.sub.B are continuous, the RNS code data D.sub.R are also changed continuously.
However, the binary code data D.sub.B which is represented when the residue data of any of the moduli of the RNS code data D.sub.R [00000 ] which stands for [0] of the binary code data proves to be 1 as shown in the following Table 2.
TABLE 2 ______________________________________ Binary Code D.sub.B Represented When Residue Data of Any of Moduli of RNS Code Data D.sub.R [00000] is 1 RNS Code Data D.sub.R Binary Code m.sub.0 m.sub.1 m.sub.2 m.sub.3 m.sub.4 Data D.sub.B ______________________________________ 0 0 0 0 0 0 1 0 0 0 0 2 0 5 9 2 0 0 1 0 0 0 1 9 6 5 6 0 0 0 1 0 0 3 6 9 6 0 0 0 0 1 0 1 7 6 1 7 6 0 0 0 0 1 1 0 5 1 0 5 ______________________________________
Thus it is seen that, when the value of the residue data of any of the moduli m.sub.0, m.sub.1, m.sub.2, m.sub.3 or m.sub.4 of the RNS code data D.sub.R is changed only by one, the value of the associated binary code data D.sub.B is changed drastically.
Hence, with the digital filter apparatus making use of the RNS system, when only one signal bit is shorted with the other signal bit or deteriorated to 0 or 1, the result of decoding becomes significantly different from the true value. For this reason, in case a malfunction occurs in a modulus series or system, it can be estimated only with difficultly in which signal bit of which modulus system the malfunctioning has occurred.